A geometric realization of the $m$-cluster category of type $\tilde{A}$

Abstract

We give a geometric realization of a subcategory of the $m$-cluster category ${\mathcal{C}}^m$ of type ${\tilde{A}}_{p,q}$, by using $(m+2)$-angulations of an annulus with $p+q$ marked points. We also give a bijection between an equivalence class of $(m+2)$-angulations and the mutation class of coloured quivers of type ${\tilde{A}}_{p,q}$.

23 pages, 16 figures

References in corpus (2)

• On triangulated orbit categories
• Counting cluster-tilted algebras of type $A_n$

Cited by in corpus (1)

• A geometric realization of tame categories